# Linear algebra: alternate coordinate systems solving

Recent questions in Alternate coordinate systems
Alternate coordinate systems

### The Cartesian coordinates of a point are given. a) $$(2,-2)$$ b) $$(-1,\sqrt{3})$$ Find the polar coordinates $$(r,\theta)$$ of the point, where r is greater than 0 and 0 is less than or equal to $$\theta$$, which is less than $$2\pi$$ Find the polar coordinates $$(r,\theta)$$ of the point, where r is less than 0 and 0 is less than or equal to $$\theta$$, which is less than $$2\pi$$

Alternate coordinate systems

### For the cuboid below: a. write down the coordinates of point B. b. write down the coordinates of point A. c. find the coordinates of the midpoint, M, of the diagonal [AO] of the cuboid.

Alternate coordinate systems

### Find the value of x or y so that the line passing through the given points has the given slope. (9, 3), (-6, 7y), $$m = 3$$

Alternate coordinate systems

### To plot: Thepoints which has polar coordinate $$\displaystyle{\left({2},\frac{{{7}\pi}}{{4}}\right)}$$ also two alternaitve sets for the same.

Alternate coordinate systems

### The system of equation \begin{cases}2x + y = 1\\4x +2y = 3\end{cases} by graphing method and if the system has no solution then the solution is inconsistent. Given: The linear equations is \begin{cases}2x + y = 1\\4x +2y = 3\end{cases}

Alternate coordinate systems

### What are polar coordinates? What equations relate polar coordi-nates to Cartesian coordinates? Why might you want to change from one coordinate system to the other?

Alternate coordinate systems

### The equivalent polar equation for the given rectangular - coordinate equation. $$\displaystyle{y}=\ -{3}$$

Alternate coordinate systems

### The reason ehy the point $$(-1, \frac{3\pi}{2})$$ lies on the polar graph $$r=1+\cos \theta$$ even though it does not satisfy the equation.

Alternate coordinate systems

### Determine if $$\left\{ \begin{bmatrix}2 \\ -4 \\1 \end{bmatrix},\begin{bmatrix}-3 \\ 5 \\ -1 \end{bmatrix} \right\}$$ is a basis for $$Col \begin{bmatrix}1 \\ -3 \\1 \end{bmatrix},\begin{bmatrix}-3 \\ 7 \\ -2 \end{bmatrix}$$

Alternate coordinate systems

### All bases considered in these are assumed to be ordered bases. In Exercise, compute the coordinate vector of v with respect to the giving basis S for V. $$V is P_1, S = {t + 1, t - 2}, v = t + 4$$

Alternate coordinate systems

### The intercepts on the coordinate axes of the straight line with the given equation $$\displaystyle{4}{x}-{3}{y}={12}.$$

Alternate coordinate systems

### All bases considered in these are assumed to be ordered bases. In Exercise, compute the coordinate vector of v with respect to the giving basis S for V. V is $$R^2, S = \left\{ \begin{bmatrix}1 \\ 0 \end{bmatrix}\begin{bmatrix} 0 \\1 \end{bmatrix} \right\}, v = \begin{bmatrix} 3 \\-2 \end{bmatrix}$$

Alternate coordinate systems

### Given V = R, and two bases: B and C and the coordinator [v]B a) Find the change of coordinates matrix $$\displaystyle{P}{B}\rightarrow{C}.$$ b) Find the coordinator [v]C.

Alternate coordinate systems

### To find: The alternate solution to the exercise with the help of Lagrange Multiplier. $$\displaystyle{x}+{2}{y}+{3}{z}={6}$$

Alternate coordinate systems

### Let A and C be the following ordered bases of P3(t): $$\displaystyle{A}={\left({1},{1}+{t},{1}+{t}+{t}^{{2}},{1}+{t}+{t}^{{2}}+{t}^{{3}}\right)}$$ $$\displaystyle{C}={\left({1},-{t},{t}^{{2}}-{t}^{{3}}\right)}$$ Find tha change of coordinate matrix $$\displaystyle{I}_{{{C}{A}}}$$

Alternate coordinate systems

### All bases considered in these are assumed to be ordered bases. In Exercise, compute the coordinate vector of v with respect to the giving basis S for V. V is $$R^2, S = \left\{ \begin{bmatrix}1 \\ 0 \end{bmatrix}\begin{bmatrix} 0 \\1 \end{bmatrix} \right\}, v = \begin{bmatrix} 3 \\-2 \end{bmatrix}$$

Alternate coordinate systems

### 1. Show that sup $$\displaystyle{\left\lbrace{1}−\frac{{1}}{{n}}:{n}\in{N}\right\rbrace}={1}{\left\lbrace{1}−\frac{{1}}{{n}}:{n}\in{N}\right\rbrace}={\frac{{{1}}}{{{2}}}}$$. If $$\displaystyle{S}\:={\left\lbrace{\frac{{{1}}}{{{n}}}}−{\frac{{{1}}}{{{m}}}}:{n},{m}\in{N}\right\rbrace}{S}\:={\left\lbrace{\frac{{{1}}}{{{n}}}}−{\frac{{{1}}}{{{m}}}}:{n},{m}\in{N}\right\rbrace},{f}\in{d}\in{f}{S}{\quad\text{and}\quad}\supset{S}.{e}{n}{d}{\left\lbrace{t}{a}{b}\underline{{a}}{r}\right\rbrace}$$

Alternate coordinate systems

### List the members of the range of the function h: $$x - 5 - 2x$$? with domain $$D = {- 2, - 1, 0, 1}$$.

Alternate coordinate systems